# 3: Conservation Laws & Concept-Based Problem Solving

Activities & Reader (ISBN 0-7872-3931-3, 224 pages)

How to Use this Book *xiii*

Acknowledgments *xv*

### Activities

- 71 - Investigating Collisions in which Two Objects Stick Together
*313* - 72 - Introducing the Concepts of Impulse and Momentum
*317* - 73 - Using Impulse and Momentum to Solve Constant-Force Problems
*321* - 74 - Analyzing Collisions Using Newton's Third Law
*325* - 75 - Relating Momentum Ideas to One-Body Problem Situations
*331* - 76 - Relating Momentum Ideas to Situations Having Two or More Objects
*335* - 77 - Reasoning with Impulse and Momentum Ideas
*339* - 78 - Solving Problems Using Momentum Principles
*343* - 79 - Summarizing and Structuring Momentum and Impulse Ideas
*347* - 80 - Recording Your Thoughts about Energy
*349* - 81 - Relating Forces to the Motion of Objects
*353* - 82 - Relating Work to Forces and Displacements
*357* - 83 - Recognizing the Presence of Work
*361* - 84 - Comparing the Work Done by Forces
*367* - 85 - Computing the Work Done by Forces
*371* - 86 - Recognizing and Comparing Kinetic Energy
*375* - 87 - Reasoning with Work and Energy Ideas
*381* - 88 - Solving Problems with the Work-Kinetic Energy Theorem
*385* - 89 - Recognizing the Presence of Potential Energy
*389* - 90 - Comparing the Potential Energy
*393* - 91 - Computing the Potential Energy
*399* - 92 - Keeping Track of Energy: The Law of Conservation of Energy
*403* - 93 - Reasoning with Energy Ideas
*411* - 94 - Solving Problems Using Energy Ideas
*415* - 95 - Summarizing and Structuring Energy Ideas
*419* - 96 - Recording Your Ideas about Problem Solutions
*421* - 97 - Recognizing the Appropriate Principle/Law
*425* - 98 - Matching Solution Strategies with Problems
*433* - 99 - Writing and Comparing Solution Strategies
*437* - 100 - Solving One-Principle Problems
*441* - 101 - Solving More Complex Problems
*445* - 102 - Structuring Mechanics
*449*

### Reader: Chapter 3 — Conservation Laws

- 3.0 Introduction
*R61*- What is meant by a conservation law?
*R61* - Why use a conservation law instead of dynamics?
*R61*

- What is meant by a conservation law?
- 3.1 SYSTEMS
*R61*- What is a system?
*R61* - Sizes of systems
*R61*

- What is a system?
- 3.2 MOMENTUM AND IMPULSE
*R62-65*- Impulse
*R62,63*- definition of impulse for constant force
*R62* - units for impulse: N-s
*R62* - how to calculate impulse for a given force and time interval
*R62,63* - definition of net impulse for constant net force
*R63* - how to calculate net impulse for constant net force
*R63*

- definition of impulse for constant force
- Momentum
*R64,65*- definition of momentum for single bodies
*R64* - how to calculate the momentum
*R64* - units for momentum: kg-m/s
*R64* - what momentum means in some common situations
*R64* - how to find the
__change__in momentum*R64,65*

- definition of momentum for single bodies

- Impulse
- 3.3 TWO PRINCIPLES FOR DESCRIBING PHYSICAL SYSTEMS AND SOLVING PROBLEMS
*R66-70*- Impulse-Momentum Theorem
*R66,67*- comparing the net impulse and the change in momentum
*R66* - equivalence of the units for impulse and the units for momentum
*R66* - statement of the Impulse-Momentum Theorem for single bodies
*R66*

- comparing the net impulse and the change in momentum
- Conservation of Momentum for two-body systems
*R68-70*- using Newton's third law to understand collisions
*R68* - using the Impulse-Momentum Theorem to understand collisions
*R69* - statement of Conservation of Momentum for no net force on system
*R69* - definition of
*total*momentum*R69* - situations in which total momentum is only
__approximately__conserved*R69,70*

- using Newton's third law to understand collisions

- Impulse-Momentum Theorem
- 3.4 USING MOMENTUM IDEAS AND PRINCIPLES TO ANALYZE SITUATIONS AND SOLVE PROBLEMS
*R70-79*- Reasoning with momentum ideas
*R70-74*- situations involving a net impulse
*R70-73*- using the Impulse-Momentum Theorem when there is a net impulse
*R71* - looking at the change in momentum
*R71* - making reasonable assumptions before making comparisons
*R72* - using limiting cases to make comparisons
*R72* - effect of mass on an object's response to an interaction
*R73*

- using the Impulse-Momentum Theorem when there is a net impulse
- situations in which the net impulse is zero or very close to zero
*R73,74*- using Conservation of Momentum when the impulse is small
*R74* - Conservation of Momentum is a vector equation
*R74*

- using Conservation of Momentum when the impulse is small

- situations involving a net impulse
- Solving problems with momentum ideas
*R75-78*- using the Impulse-Momentum Theorem to solve problems
*R75,76*- two different ways of using the Impulse-Momentum Theorem
*R75* - Impulse-Momentum Theorem for constant net force
*R75* - four types of quantities: forces, time intervals, masses, velocities
*R75* - representation of problem solving using the Impulse-Momentum Theorem
*R76*

- two different ways of using the Impulse-Momentum Theorem
- using Conservation of Momentum to solve problems
*R76-78*- four common steps for solving Conservation of Momentum problems
*R76* - Conservation of Momentum is a vector equation
*R77,78* - representation of problem solving using Conservation of Momentum
*R78*

- four common steps for solving Conservation of Momentum problems

- using the Impulse-Momentum Theorem to solve problems
- Summary of momentum ideas and principles
*R79*- one new
*state*quantity: momentum**p***R79* - two new
*process*quantities: impulse**J**, and__change__in momentum D**p***R79* - two new physical principles: the Impulse-Momentum Theorem and Conservation of Momentum
*R79* - new energy ideas:
*work, kinetic energy, potential energy**R79* - limitations of momentum ideas
*R79*

- one new

- Reasoning with momentum ideas
- 3.5 WORK AND KINETIC ENERGY
*R80-90*- Definition of work
*R80-84*- What factors affect the way a force changes the speed of something?
*R80* - definition of work for a constant force using the component of the force parallel to the displacement
*R80* - work is a scalar quantity
*R81* - units for work: J (joule)
*R81* - calculating the work done by a constant force
*R81* - how the work done can be negative
*R81* - What happens when the force is perpendicular to the displacement?
*R81* - circumstances when a different definition of work is needed
*R82* - definition of work for a constant force using the component of the displacement parallel to the force
*R82* - definition of total work
*R83,84*

- What factors affect the way a force changes the speed of something?
- Calculating the work done by common forces
*R84-89*- work done by the gravitational force
*R84*- depends on the mass, the gravitational constant (
*g*), and the__change__in height*R84* - why there is a minus sign in the expression
*R84*

- depends on the mass, the gravitational constant (
- work done by the normal force
*R85,86*- why the normal force often does no work on an object
*R85* - situations in which the normal force does work on an object
*R85* - the
__total__work done by the normal force is always zero*R85* - how the normal force can do no work even when it delivers an impulse
*R86*

- why the normal force often does no work on an object
- work done by the tension force
*R86,87*- why the tension force often does no work on an object
*R86* - situations in which the tension force does work
*R86,87* - the
__total__work done by the tension force is always zero*R87*

- why the tension force often does no work on an object
- work done by the friction force (static and kinetic)
*R88*- the static friction force can do work on isolated objects
*R88* - the static friction force can do no
__total__work*R88* - why we cannot calculate the work done by kinetic friction
*R88*

- the static friction force can do work on isolated objects
- work done by the spring force
*R89*- using a graph of force vs. displacement to find the work done
*R89* - the graph of force vs. displacement is often a straight line
*R89*

- using a graph of force vs. displacement to find the work done

- work done by the gravitational force
- Kinetic energy
*R90,91*- What changes when total work is done on an object?
*R90* - definition of kinetic energy
*R90* - circumstances under which the kinetic energy changes
*R91* - definition of
__total__kinetic energy*R91*

- What changes when total work is done on an object?

- Definition of work
- 3.6 TWO MORE PRINCIPLES FOR DESCRIBING PHYSICAL SYSTEMS AND SOLVING PROBLEMS
*R92-99*- Work-Kinetic Energy Theorem
*R92-94*- Statement of the Work-Kinetic Energy Theorem
*R92* - depends on the
__total__work and the__change__in__kinetic__energy*R92* - statement of the Work-Kinetic Energy Theorem for a system of objects
*R92* - depends on the total work and the change in
__total__kinetic energy*R92* - this is a scalar equation
*R92* - using the Work-Kinetic Energy Theorem to find the speed of something
*R92,93* - sometimes the forces doing work are hard to determine
*R94* - more reasons why we cannot calculate the work done by kinetic friction
*R94*

- Statement of the Work-Kinetic Energy Theorem
- Conservation of Energy
*R95-99*- statement of the Law of Conservation of Energy
*R95* - why we need two new kinds of energy:
*potential energy*and*microscopic energy**R95*

- statement of the Law of Conservation of Energy
- Potential energy
*R95-98*- change in gravitational potential energy
*R95* - gravitational potential energy for objects near the surface of celestial bodies
*R95* - using a reference height to determine the gravitational potential energy
*R95* - gravitational potential energy does not depend upon motion
*R96* - gravitational potential energy can be negative
*R96* - finding the potential energy stored in a spring
*R97* - factors affecting the spring potential energy
*R97,98* - the spring potential energy is always positive
*R98*

- change in gravitational potential energy
- Microscopic vs. macroscopic energy
*R98,99*- definitions of the microscopic and macroscopic realms
*R98* - how energy is contained in the microscopic realm
*R98,99* - definition of total energy
*R99* - Law of Conservation of Energy
*R99*

- definitions of the microscopic and macroscopic realms

- Work-Kinetic Energy Theorem
- 3.7 USING ENERGY IDEAS AND PRINCIPLES TO ANALYZE SITUATIONS
*R100-105*- Analyzing situations using the Work-Kinetic Energy Theorem
*R100,101*- whenever the kinetic energy of something changes, work is done
*R100* - difficulties in identifying the forces actually doing work
*R100,101* - similarities and differences between momentum and kinetic energy
*R101*

- whenever the kinetic energy of something changes, work is done
- Analyzing situations using Conservation of Energy
*R102-106*- why the law is not particularly useful without modification
*R102* - Work-Energy Theorem (for a system of objects)
*R102* - definition of
*external*work*R102* - different ways of looking at the same situation
*R102-104* - using dynamics and kinematics to analyze a situation before applying Conservation of Energy
*R104* - where the energy goes during a collision
*R104,105* - change in microscopic energy due to friction
*R105* - different situations that may be used to derive the change in microscopic energy due to friction
*R105* - change in microscopic energy due to air resistance
*R106*

- why the law is not particularly useful without modification

- Analyzing situations using the Work-Kinetic Energy Theorem
- 3.8 USING ENERGY IDEAS AND PRINCIPLES TO SOLVE PROBLEMS
*R106-113*- Solving problems using the Work-Kinetic Energy Theorem
*R106-109*- two procedures for solving problems
*R106-108* - representation of problem solving using the Work-Kinetic Energy Theorem
*R108,109*

- two procedures for solving problems
- Solving problems using Conservation of Energy
*R109-113*- similarities and differences between the Work-Kinetic Energy Theorem and the Work-Energy Theorem
*R109* - problems in which the total work done by external forces is zero or negligibly small
*R110,111* - problem in which the total work done by external forces in non-zero
*R112* - why the Work-Energy Theorem is how we apply Conservation of Energy to a system of objects
*R113* - representation of problem solving using Conservation of Energy
*R113*

- similarities and differences between the Work-Kinetic Energy Theorem and the Work-Energy Theorem
- Summary of energy ideas and principles
*R113*- many new state quantities: kinetic, potential, and microscopic energy
*R113* - many new process quantities: work, changes in state quantities
*R113* - one new physical law: Conservation of Energy
*R113* - two new problem-solving principles: the Work-Kinetic Energy Theorem and the Work-Energy Theorem
*R113*

- many new state quantities: kinetic, potential, and microscopic energy
- Summary of conservation laws
*R113-114*- reasons for using conservation laws
*R113* - how scientists apply conservation laws to new situations
*R114* - what we will do as we study new areas of physics
*R114*

- reasons for using conservation laws

- Solving problems using the Work-Kinetic Energy Theorem

### Reader: Chapter 4 — Concept-Based Problem Solving

- 4.0 Introduction
*R115*- Some questions you might ask yourself before solving a problem
*R115* - Why a conceptual analysis should precede equation manipulation
*R115*

- Some questions you might ask yourself before solving a problem
- 4.1 A PHYSICIST'S VIEW OF MECHANICS
*R116-121*- Explanation
*R116*- What is meant by a "view of mechanics"
*R116* - what is meant by an "organizational structure"
*R116* - what motivates a physicist's organizational structure
*R116*

- What is meant by a "view of mechanics"
- Prioritizing ideas in mechanics
*R116-120*- chronological list of many of the physics concepts learned so far
*R116* *physical principles*, the most widely useful ideas in physics*R117**concepts*, the ideas needed to understand principles*R117**equations*, the relationships needed to apply concepts and principles (*physical laws*,*definitions*,*empirical laws*, and*derived relations*)*R117,118*- a priority scheme for physics ideas, with examples
*R118,119* - other ideas relevant for solving problems (mathematical principles, operations, and problem-solving techniques)
*R119,120*

- chronological list of many of the physics concepts learned so far
- Interconnecting ideas in mechanics
*R121*- using concepts to organize knowledge
*R121*

- using concepts to organize knowledge

- Explanation
- 4.2 CONCEPT-BASED PROBLEM SOLVING
*R121-126*- How to
__start__solving a problem*R121-123*- the first three steps of concept-based problem solving
*R121,122*- step 1: sort the principles
*R121,122* - step 2: choose a principle
*R122* - step 3: apply the chosen principle and solve for the unknown
*R122*

- step 1: sort the principles
- solution to the sample problem
*R122,123*

- the first three steps of concept-based problem solving
- How to
__finish__solving a problem*R124-126*- four suggestions for efficient and effective problem solving
*R124,125*- create sketches and diagrams
*R124* - count the number of equations and unknowns
*R124* - challenge your assumptions
*R124,125* - check your answer
*R125,126*

- create sketches and diagrams

- four suggestions for efficient and effective problem solving
- Conclusion
*R126*- representation of the concept-based problem-solving approach
*R126*

- representation of the concept-based problem-solving approach

- How to

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